How to find the domain of the sine

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ACT Math › How to find the domain of the sine

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What is the domain of the given trigonometric function:

$z(t) = 2\sin(-2t)$

$(-\infty,\infty)$

CORRECT

$[-\pi,\pi]$

$[0,\infty]$

Explanation

For both Sine and Cosine, since there are no asymptotes like Tangent and Cotangent functions, the function can take in any value for . Thus the domain is:

$(-\infty,\infty)$

Find the domain of the function: $y=-9\sin(5\theta-3)-3$

${}(-\infty,\infty)$

CORRECT

$\left[-\frac{2\pi}{5},\frac{2\pi}{5}\right]$

$\left(-\frac{2\pi}{5},\frac{2\pi}{5}\right)$

$\left(-\frac{2\pi}{5},\infty\right)$

$\left(-\frac{5}{3},\frac{2\pi}{5}\right)$

Explanation

The function $y=-9\sin(5\theta-3)-3$ is related to the parent function $y=\sin(\theta)$ , which has a domain of $(-\infty.\infty)$ .

The value of theta for $y=-9\sin(5\theta-3)-3$ has no restriction and is valid for all real numbers.

The answer is $(-\infty,\infty)$ .

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